Here's an alternative to imw (an implementation of the extended
euclidean algorithm):
eeu=: [: , (] ,: (1 1 1 0*[) - <.@%&{. * (1 1 1
0^~]))/^:(*@{.@{:)^:_@(,.&(x:=0 1 0))
Example use:
eeu 11 3
1 _1 4 _1 0 3 _11 _2
Note, however, that the result is structured differently:
The result of (4 { imw^:_ ] ,~ 1 0 0 1x) is 0 { eeu
(But the result of (2 { imw^:_ ] ,~ 1 0 0 1x) is 2 { eeu)
I'm still playing around with these ideas, and trying to digest them,
and the performance of this approach isn't really all that different.
But I sort of like the way this expression looks.
Thanks,
--
Raul
On Wed, Jan 29, 2014 at 3:02 PM, Pascal Jasmin <godspiral2...@yahoo.ca> wrote:
> Here is the first invmod method
>
> invmod=: 4 : 0
> NB. inverse of y mod x (x|y)
> NB. uc vc ud vd d c where d c init as x y
> NB. q =. d<.@%c -- (4&{ <.@%~ {:)
>
> a=. imw^:_ ] 1x,0x,0x,1x,x,y
> if. 1~: 4{a do. 0 return. end.
> if.0< 2{ a do. 2{ a else. x+2{a end.
>
> )
> imw =: ((2&{ - {. * 4&{ <.@% {:),(3&{ - 1&{ * 4&{ <.@% {:), 2&{., ({: | 4&{)
> ,~{:)^:(0 ~: {:)
> testinvmod =: (0 1 e.~ [ | ]* invmod)
>
> 11 invmod 3
> 4
>
> (14114588 +i.10) ( invmod)"0 1 ] 3x
> 4704863 0 9409727 4704864 0 9409729 4704865 0 9409731 4704866
>
> ts '(14114588x +i.10000) (testinvmod )"0 ] 3x'
> 2.74558/sec 3.14547MB
> ts '(14114588 +i.10000) (invmod )"0 ] 3'
> 2.96905/sec 3.26822MB
>
>
> ----- Original Message -----
> From: Pascal Jasmin <godspiral2...@yahoo.ca>
> To: "programm...@jsoftware.com" <programm...@jsoftware.com>
> Cc:
> Sent: Wednesday, January 29, 2014 11:35:19 AM
> Subject: [Jprogramming] math requests
>
>
>
> With all of the mathematicians on this list, these functions have likely been
> implemented before in J.
>
> elyptic curve point add, multiplication and double
> a python reference implementation:
> https://github.com/warner/python-ecdsa/blob/master/ecdsa/ellipticcurve.py
>
> the functions are: __add__ __mul__ and double
>
> if I may suggest J explicit signatures for the first 2 functions as:
>
> F =: 4 : 0
> 'yx yy yo' =. y
> 'xx xy xo' =. x
> )
>
> Some other methods than the python reference could be considered here:
>
> http://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication
>
>
> also appreciated if you have in implementation of inverse_mod
> for reference function of same nate at:
> https://github.com/warner/python-ecdsa/blob/master/ecdsa/numbertheory.py
>
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